The quadratic formula is a mathematical equation used to find the solutions of a quadratic equation, which is typically in the form ax^2 + bx + c = 0 . The formula is expressed as x = \frac-b \pm \sqrt{b^2 - 4ac}2a , where a , b , and c are constants. The symbol \pm indicates that there can be two possible solutions for x . The discriminant, represented by b^2 - 4ac , determines the nature of the solutions. If the discriminant is positive, there are two distinct real solutions. If it is zero, there is exactly one real solution, and if it is negative, the solutions are complex or imaginary numbers. The quadratic formula is a fundamental tool in algebra for solving various problems involving parabolas.